Linear Models

  1. Model Diagnostics and Assumption Checking
    1. Assumptions of Linear Regression
      1. Linearity
        1. Definition and Importance
          1. Consequences of Violation
          2. Independence of Errors
            1. Consequences of Violation
            2. Homoscedasticity
              1. Constant Variance of Errors
                1. Consequences of Heteroscedasticity
                2. Normality of Errors
                  1. Importance for Inference
                    1. Assessing Normality
                  2. Graphical Diagnostics
                    1. Residuals vs. Fitted Values Plot
                      1. Identifying Non-linearity
                        1. Identifying Heteroscedasticity
                        2. Normal Q-Q Plot
                          1. Assessing Normality of Residuals
                          2. Scale-Location Plot
                            1. Detecting Non-constant Variance
                            2. Residuals vs. Leverage Plot
                              1. Identifying Influential Points
                            3. Detecting and Handling Violations
                              1. Non-linearity
                                1. Residual Plot Patterns
                                  1. Transformations of Predictors
                                    1. Log Transformation
                                      1. Polynomial Terms
                                        1. Other Transformations
                                      2. Heteroscedasticity
                                        1. Visual Detection
                                          1. Formal Tests
                                            1. Weighted Least Squares
                                              1. Transformations of Response Variable
                                              2. Non-normality of Residuals
                                                1. Visual Detection
                                                  1. Formal Tests
                                                    1. Robust Regression Methods
                                                    2. Correlated Errors
                                                      1. Detection Methods
                                                        1. Durbin-Watson Test
                                                          1. Time Series Considerations
                                                        2. Outliers and Influential Points
                                                          1. Identifying Outliers
                                                            1. Studentized Residuals
                                                              1. Definition and Calculation
                                                              2. Measuring Leverage
                                                                1. Hat Values
                                                                  1. Definition and Calculation
                                                                  2. Measuring Influence
                                                                    1. Cook's Distance
                                                                      1. DFFITS
                                                                        1. DFBETAS
                                                                        2. Strategies for Handling Influential Points
                                                                          1. Investigating Data Quality
                                                                            1. Model Robustness Checks
                                                                              1. Data Exclusion or Transformation

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                                                                          4. Multiple Linear Regression

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                                                                          6. Model Building and Variable Selection